 Radioactive activity

With $n$ parent atomic nuclei present, the conditional expected number of transformations in a short interval is approximately $\lambda n\Delta t$. The corresponding radioactive activity is $A=\lambda n$. Averaging over the finite-population radioactive decay model gives $\overline{A}(t)=\lambda \overline{N}(t)$. Its unit is the becquerel.^[ref]

For a finite counting interval, depletion matters. Suppose each transformation is recorded independently with detection efficiency $\epsilon$, with at most one count per transformation and no background. The expected value of the count between $t$ and $t+\Delta t$ isOnly when $\lambda \Delta t\ll 1$ does this become approximately $\epsilon \overline{A}(t)\Delta t$. A count rate therefore needs a detector model before it can be interpreted as the source's radioactive activity.